If eChess doesn't work because all of it is electronic and Correspondence doesn't work because snail mail is not involved then the previous mentioned email-chess should serve as the modern version of correspondence without implying that it's live.

(I do not know whether is was named in the above 204 earlier postings).

Why: since indeed lots of players would not realy understand the characterization 'Correspondence Chess' + TURN BASED represents is in fact somehow the 'opposite' of 'instant chess/ live chess' which is in use for the one of the other forms of conducting style of playing chess.

We still happily use the term 'correspondent' to refer to news reporters who have long since given up the practice of sending their reports via the postal system.

Why is it so hard to allow users of chess.com to take for granted the fact that their 'correspondence' won't require any stamps to be licked?

Despite my little jest above, OCC is a good description. But I guess that the site doesn't want to use an abbreviation and the whole lot is too long, so that just brings us back to CORRESPONDENCE CHESS.